The pattern elements to be measured are, in particular, opaque or transparent regions on mask surfaces or patterns on wafers that are used for semiconductor manufacture. The pattern elements to be measured have different widths and lengths and are distinguishable, for example, by way of the location, height, and orientation of their edges. In order to indicate the position of a pattern element on the substrate, often the mutually parallel edge locations are measured and the position is indicated as the centerline with respect to the two edges. In the case of a pattern element measurable as to width and length, or that of two intersecting pattern elements, the position is indicated by way of the coordinates of the intersection point of the two centerlines. Edge position determination is of particular significance because measurement errors have a direct impact on the production process. A measurement accuracy on the nanometer scale is therefore demanded by the semiconductor industry.
Measurement of edge positions is accomplished in special coordinate measuring instruments. A measuring instrument suitable for carrying out the known method is described, for example, in the paper of Dr. Carola Bläsing entitled “Pattern Placement Metrology for Mask Making,” presented at the Education Program of Semicon Geneva on Mar. 31, 1998.
An example of a typical measuring instrument is described below. The substrate having the pattern element is mounted on a displaceable measurement stage whose position in a measurement plane relative to a reference point can be measured interferometrically. An imaging system is arranged with its optical axis perpendicular to the measurement plane, and images a substrate region having the pattern element onto a detector array in magnified fashion.
The pixels of the detector array are oriented in rows and columns parallel to the axes of an X-Y coordinate system associated with the substrate. The position of the edge of the pattern element is determined, relative to the reference point, in the coordinate system defined on the substrate; the point at which the optical axis of the imaging system strikes the substrate usually serves as the reference point. The detector array is generally oriented in such a way that its center coincides with the reference point. The location of the substrate coordinate system is aligned, using alignment marks, relative to the measurement instrument coordinate system. Usually the edge of the pattern element to be measured is also oriented parallel or perpendicular to the axes of the mask coordinate system, and thus also to the rows and columns of the detector array.
The image, acquired with the detector array, of the pattern element having the edge is analyzed using image-analysis methods. Using a rectangular measurement window generated in software, a specific region of the detector array, i.e. an image area, is selected for measurement. The measurement window is preferably placed transversely to an edge to be measured of the pattern element.
The contrast level of the edge image varies as a function of the resolution and imaging quality of the imaging system. The best contrast is set using a TV autofocus system. Within a measurement window, the intensities of the pixels lying in one particular row or column parallel to the edge of the pattern element are averaged. This yields an intensity profile of the edge image, perpendicular to the edge, over one row or column of pixels. This intensity profile illustrates the intensity as a function of the location in the measurement direction that is defined perpendicular to the edge.
The location of the edge is defined, for example, by means of a predetermined parameter of the aforesaid intensity profile, for example at 50% of maximum intensity. The interpolated pixel row or pixel column on which the edge is located relative to the reference point is indicated as the resulting edge location. The edge position is thus determined with pixel accuracy.
Determination of the edge location in the calculated intensity profile is of particular importance. In known methods, an edge is assumed to exist in the region of an intensity profile that exhibits a sharp rise or fall in intensity. In this region, a straight-line fit is performed with the individual values of the intensity profile. The problem is that depending on the length of the fitted region and the consequently varying number of individual intensity profile values used for the straight-line fit, the fit can assume different slopes. With different slopes, however, the parameter for determination of the edge position—which is located, for example, at 50% of the maximum intensity—is located at different points, i.e. pixels which correspond to a specific position on the substrate. Calculation of the straight-line fit therefore already constitutes a considerable error in edge determination.
Another problem results from the fact that the measured curve shape of the intensity profile depends, among other factors, on the width and height of the patterns and on the imaging aperture. With optical image acquisition, for example, it is advantageous if the illumination aperture is small compared to the observation aperture. This yields maximum steepness of the intensity profile at the location of the edge, so the position is better defined. Overshoots then occur in the profile, however.
With very narrow patterns, shadow lines of the pattern occur in the intensity profile and supply additional minima that coincide when the pattern lines are particularly narrow (e.g. on wafers). With the straight-line fit method, only the positions of the outer boundaries of the shadow lines can be determined, but a reliable determination of the position of the actual edges of the pattern element is not possible.
U.S. Pat. No. 5,136,661 describes a method for determining edge position. The method defines, for the edge being sought, a straight line with a defined slope. From the image of the pattern, an intensity profile is determined in known fashion, and a measured straight-line fit is calculated therein for each edge contained in it. A variety of evaluation variables are calculated; these are used to select the edge whose measured straight-line fit exhibits the least deviation from the model edge. Selection of the most similar edge is, however, very complex and calculation-intensive. In some cases it requires prior knowledge of the existing pattern widths (e.g. reference widths from the manufacturing process). In addition, the determination of edge position is made with only pixel accuracy, and the problem described above of the straight-line fit on critical intensity profiles remains unresolved.